I’ve gotten into a discussion about PowerBall odds with a few friends over the last few days, and I noted that the numbers I was flinging about were for the old rules before they made it harder to win (and enabling more frequent prizes in the $200 million range).

All in all, what’s not true is that PowerBall is always a losing game, as can be determined from the posted odds. What is true is that the people who play it all the time are contributing their equity to the people who only come on board when the prize is big.

The straight odds at the beginning of the cycle are truly horrible: a $10M prize has a cash value of $5.7 million, which yields an expectation of $0.22 for every dollar wagered. If you play the Power Play (which multiplies a win from 2x to 5x for a $2 bet), the expectation is $0.376.

Needless to say, since doubling your bet will always at least double any prize other than the jackpot, you should always bet the Power Play.

Working upwards from there, and assuming that the cash value of the prize relative to the posted value is constant (it’s not, but fairly close), a normal $1 ticket wins more than a dollar on average when the jackpot is $174,803,787. Power Players can jump in when the prize hits $141,821,769.

Naturally, this skips some issues:

1. The whole system betrays the law of large numbers, which is to say that you won’t live long enough to play enough games to have a reasonable expectation of winning. Another way of phrasing this is that most people won’t bet a million dollars to win a billion on a coin flip. Even if the game is in your favor, large numbers make the betting considerations less than purely mathematical.
2. Prizes are split when the prize is won by more than one person. This is fairly rare, but reduces the effective expectation of the winner by some amount I can’t be bothered to calculate.
3. PowerBall has a bizarre pool system that spreads some jackpot money into the other wins when the prize gets very large. This increases the expectation of the winner by some amount I can’t be bothered to calculate.

But rule of thumb, when the prize hits $140 million, go ahead and buy a $2 ticket.